Andrea Leadsom, the leader of the House of Commons, is to make a statement to MPs on allegations of sexual harassment by ministers and MPs at Westminster, as the government comes under pressure to show it is investigating the claims.

Theresa May is expected to be alongside Leadsom in the Commons on Monday afternoon and her spokesman said she was “deeply concerned” by the allegations.

The spokesman pointedly declined to confirm that May had full confidence in the international trade minister Mark Garnier, who is the subject of an internal government inquiry into sexually suggestive comments he made to his secretary.

May has announced an inquiry into the conduct of Garnier, and written to the Speaker of the Commons, John Bercow, to seek better ways for MPs’ staff to raise concerns about their employers.

But amid reports of several dozen Tory MPs and ministers being named as behaving in a sexually inappropriate way on a list drawn up by party aides, May’s spokesman declined to say whether she had sought information on potential wrongdoing.

May’s spokesman denied that the prime minister had seen an alleged dossier compiled by party whips on MPs’ behaviour, saying: “There is no dossier and therefore the prime minister hasn’t seen one.” He added that he could not give a “running commentary” on what was happening.

He said he did not know of any allegations of wrongdoing beyond that connected to Garnier, who has admitted asking a former assistant to buy sex toys and calling her “sugar tits”.

Asked if May had sought information from her whips on other allegations, her spokesman said: “I’m not going to get into details of every conversation that may or may not have taken place.

“What’s very clear from the prime minister is that she’s deeply concerned at the recent media reports regarding the alleged mistreatment of staff by some members of parliament.

“She’s been clear any unwanted sexual behaviour is completely unacceptable in any walk of life, and she strongly believes it’s important that those who work in parliament are treated properly and fairly, as would be expected in any modern workplace.

“That’s why she’s written to the Speaker to ask for his support in what can be done to ensure the reputation of parliament isn’t damaged by these allegations of impropriety.”

The spokesman denied that this amounted to a reactive approach, saying: “It’s very clear the prime minister is taking this very seriously.“

He said he could not comment further on the review into Garnier’s alleged behaviour, which is being carried out by the Cabinet Office on the basis of the ministerial code of conduct, except to say that it would be completed as quickly as possible.

Asked if May would expect ministers to resign if they had committed sexual misconduct, he said: “The prime minister has been clear that this type of behaviour would be inappropriate if proven, and that appropriate action should be taken.”

Meanwhile, the former work and pensions secretary Stephen Crabb has apologised for “sexual chatter” with a 19-year-old who had applied for a job in his office.

Labour’s shadow minister for women and equalities, Dawn Butler, wrote to May on Monday asking whether Garnier and Crabb would be investigated by the Conservative party, and would have the whip withdrawn while this took place.

Butler said she was “extremely concerned” at the reports the prime minister had been briefed about wrongdoing, and asked whether May knew about any other cases.

Butler added: “Sunday newspaper reports claim that you are concerned that taking action against ministers could risk the government collapsing. All party political considerations should be put to one side to ensure we take serious action.”

On Sunday, May wrote to Bercow calling on him establish an independent mediation service for staff wanting to raise concerns about MPs’ behaviour and to enforce a grievance procedure, which is currently voluntary.

The Independent Parliamentary Standards Authority recommends that a grievance procedure is included in employees’ contracts. However, parliamentary staff work directly for MPs, who are in effect self-employed and do not have to adopt the policy.

“It does not have the required teeth, as contractually an MP does not have to follow the procedure. I do not believe this situation can be tolerated any longer,” May said in her letter.

A series of claims about the behaviour of senior politicians have emerged in recent days, after the Harvey Weinstein scandal encouraged women in other professions to share their experiences.

Garnier, the Conservative MP for Wyre Forest in Worcestershire, did not deny the events detailed by his former assistant Caroline Edmondson in the Mail on Sunday.

“I’m not going to be dishonest,” Garnier said. He insisted that referring to Edmondson as “sugar tits”, as she says he did, was a reference to the BBC comedy Gavin and Stacey, saying: “It absolutely does not constitute harassment.” Neither did he deny encouraging her to buy two sex toys in Soho, standing outside the shop while she made the purchase.

Labour MPs believe more allegations will emerge on their own side. The Sheffield Hallam MP, Jared O’Mara, was suspended from the party last week for a series of misogynistic and homophobic remarks on social media.

May’s call for a mediator follows demands from the Labour MPs John Mann and Sarah Champion for staff to be able to report allegations to an independent authority, particularly when the person harassing them may be their boss.

Mann has threatened to name a parliamentary colleague who he said was thrown off a foreign trip for harassing women.